%0 Conference Proceedings %T Optimal Trajectories of a UAV Base Station Using Lagrangian Mechanics %+ Réseaux, Mobilité et Services (RMS) %+ Département Informatique et Réseaux (INFRES) %+ Orange Labs [Lannion] %+ Laboratoire Traitement et Communication de l'Information (LTCI) %A Coupechoux, Marceau %A Darbon, Jérôme %A Kélif, Jean-Marc %A Sigelle, Marc %< avec comité de lecture %Z CDKS:Infocomwkshp-19 %( IEEE International Conference on Computer Communications (INFOCOM), Workshop on Mission-Oriented Wireless Sensor, UAV and Robot Networking (MISARN) %B IEEE International Conference on Computer Communications (INFOCOM), Workshop on Mission-Oriented Wireless Sensor, UAV and Robot Networking (MISARN) %C Paris, France %P 1-6 %8 2019-04 %D 2019 %Z Computer Science [cs]/Networking and Internet Architecture [cs.NI] %Z Mathematics [math]/Optimization and Control [math.OC]Conference papers %X This paper considers the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). A map is considered, characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. The problem is formulated using the framework of Lagrangian mechanics. When the traffic intensity is quadratic (single-phase), we derive closed-form formulas for the optimal trajectory. When the traffic intensity is bi-phase, necessary conditions of optimality are provided and an Alternating Optimization Algorithm is proposed, that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how the trajectory is improved with respect to the MPC solution. %G English %L hal-02288564 %U https://hal.telecom-paris.fr/hal-02288564 %~ INSTITUT-TELECOM %~ ENST %~ INSMI %~ TELECOM-PARISTECH %~ PARISTECH %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ TELECOM-PARISTECH-SACLAY %~ LTCI %~ INFRES %~ RMS %~ INSTITUTS-TELECOM